Two electric dipoles of dipole moments $1.2 \times 10^{-30}$ C m and $2.4 \times 10^{-30}$ C m are placed in two different uniform electric fields of strengths $5 \times 10^{4}$ NC$^{-1}$ and $15 \times 10^{4}$ NC$^{-1}$ respectively. The ratio of maximum torque experienced by the electric dipoles will be $\frac{1}{x}$. The value of $x$ is _____.

JEE Main · 2022 · 28 Jul 2022 · Shift 1 · Electrostatics

Two electric dipoles of dipole moments

1.2 \times 1 0^{- 30}

C m and

2.4 \times 1 0^{- 30}

C m are placed in two different uniform electric fields of strengths

5 \times 1 0^{4}

^{- 1}

and

15 \times 1 0^{4}

^{- 1}

respectively. The ratio of maximum torque experienced by the electric dipoles will be

\frac{1}{x}

. The value of

x

is _____.

Answer: 6

The maximum torque on an electric dipole in a uniform electric field is given by

τ_{max} = pE

, where

p

is the dipole moment and

E

is the electric field strength.

For the two dipoles:

τ_{1} = p_{1} E_{1} = 1.2 \times 1 0^{- 30} \times 5 \times 1 0^{4}

τ_{2} = p_{2} E_{2} = 2.4 \times 1 0^{- 30} \times 15 \times 1 0^{4}

The ratio:

\frac{τ _{1}}{τ _{2}} = \frac{1.2 \times 5}{2.4 \times 15} = \frac{6}{36} = \frac{1}{6}

Therefore,

x = 6

JEE Main · 2022 · 28 Jul 2022 · Shift 1 · Integer answer